RIO DE JANEIRO—A single federal judge has overseen the adjudication of Brazil’s vast corruption scandal involving state-run oil company Petróleo Brasileiro SA, issuing a string of warrants and multiyear prison sentences against some of the country’s most powerful executives.

In the process, Sergio Moro has become in the past year something of a cult figure in Brazil. Magazines regularly feature him on their covers. During recent antigovernment protests demonstrators held life-size puppets of him and signs saying, “Moro, the...